Speed up Bletchley Park genius, providing support (9)
I believe the answer is:
nurturing
'providing support' is the definition.
(to nurture something is to support it)
'speed up bletchley park genius' is the wordplay.
'speed' becomes 'run' (running is a kind of speeding).
'up' is a reversal indicator (in down clue: letters go upwards).
'bletchley park genius' becomes 'Turing' (mathematician Alan Turing).
'run' in reverse letter order is 'nur'.
'nur'+'turing'='NURTURING'
(Other definitions for nurturing that I've seen before include "Rearing; cherishing" , "Training up" .)